I wound up running over one of those temporary road signs this morning on my way into work. Damn wind knocked it over and on to the road surface. My option was to side swipe someone trying to avoid it, or run over it...which I did. End result messed up rim. The sign also cut the tire side wall.

...questions is, do I need a new tire? Should I trim the piece or rubber off or leave it?

Based on the one picture it looks like only the rim protector was ripped. Like Daft has already suggested, get the tire and rim inspected, and the wheel rebalanced (after the rim is repaired/replaced).